Mean Squared Error

Mean squared error (MSE) is a loss function that calculates the mean squared difference between the predicted and true values. It is commonly used in regression problems to evaluate the performance of a model.

Here is an example of how you can calculate the mean squared error in Python:

import numpy as np

# Calculate mean squared error
def mean_squared_error(predictions, true_values):
    squared_errors = (predictions - true_values)**2
    mean_squared_error = np.mean(squared_errors)
    return mean_squared_error

predictions = [1, 2, 3]
true_values = [0, 2, 2]
mse = mean_squared_error(predictions, true_values)
print(mse)  # Output: 0.6666666666666666

In this example, the mean squared error is calculated for a list of predictions and true values. The mean squared error is calculated as the mean of the squared differences between the predictions and true values.

You can also use the mean squared error loss function in Python with the Keras library. Here is an example of how you can use it as part of the compilation step when training a model:

from tensorflow.keras.losses import MeanSquaredError

model.compile(loss=MeanSquaredError(), optimizer='sgd')

This will cause the model to minimize the mean squared error between the predicted and true values during training.